Stress and Failure Analysis of Fiber-Reinforced Composite Structures with Computer-Based Solutions

Stress and Failure Analysis of Fiber-Reinforced Composite Structures with Computer-Based Solutions

(Emphasis on Classical Lamination Theory)

Course Outline

This eight hour online course focuses on presenting a well established computational method for calculating stresses/strains in reinforced laminated composite structures. The basis for the presented computational method is often referred to as classical lamination theory. A clear understanding of this approach is supported by the development of the fundamental mechanics of an orthotropic lamina (ply). Various failure theories are presented each requiring that stresses/strains be quantified on a ply-by-ply basis in order to make failure predictions. Both applied loads and hygrothermal (thermal and moisture) effects are treated in the computational procedure. Computer results presented herein have been produced using the LAMCALCS computer program. Use of the program is demonstrated through sample input and output descriptions. The stress and failure prediction methodology presented in this course is particularly important during the preliminary design phase of laminated composite structures.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

Learning Objective

At the conclusion of this course, the student will learn:

Understanding the differences between isotropic, orthotropic and anisotropic material behavior;
Having knowledge of the material constants required to define Hooke’s law for an orthotropic lamina (ply);
Understanding the restrictions on the material constants required in evaluating experimental data;
Knowing the difference between reference and natural (material) coordinates for an orthotropic lamina;
Being familiar with the stress-strain relations in reference and natural coordinates for an orthotropic lamina;
Understanding the coordinate transformations used in transforming stresses and/or strains from one coordinate system to another;
Knowing generally the types of tests performed to determine the stiffness and strength properties of an orthotropic lamina;
Having knowledge of a number of biaxial strength (failure) theories used in the design of laminated composite structures;
Understanding which in-plane strength quantities are needed, as a minimum, in applying various failure theories;
Knowing the difference between separable and generalized failure theories;
Understanding that the maximum stress and maximum strain failure theories make similar predictions except under certain material behavior;
Appreciating under what conditions the Chang failure criteria reduces to the Hashin failure criteria;
Knowing the basis for the fact that the Tsai-Wu failure criteria is more general than the Tsai-Hill failure criteria;
Being familiar with the effect of the direction of shear stress on lamina strength;
Understanding the laminate orientation code used to define stacking sequence;
Being familiar with a number of special laminate constructions designed to eliminate undesirable composite material behavior;
Understanding the computational procedure for determining the stresses/strains in a laminated composite subject to applied loads and/or hygrothermal effects;
Understanding the computational procedure for making failure predictions associated with stresses/strains;
Having knowledge of the basis for and limitations of classical lamination theory;
Having knowledge of the basis for and limitations of the various failure theories;
Appreciating the essential features of the computer flow chart consistent with application of classical lamination theory;
Understanding the input procedure for the LAMCALCS computer program;
Understanding the output provided by the LAMCALCS computer program; and
Understanding the importance of using consistent units in obtaining relevant stress/strain and failure predictions using LAMCALCS.

Intended Audience

This course is intended for structural, mechanical, aerospace and civil engineers.

Benefit to Attendees

Attendee of this course will be able to perform preliminary stress and failure analysis of laminated composite structures which is an essential part of the design process.

Course Introduction

This course focuses on presenting a well established computational method for calculating stresses/strains in reinforced laminated composite structures. The basis for the presented computational method is often referred to as classical lamination theory. A clear understanding of this approach is supported by the development of the fundamental mechanics of an orthotropic lamina (ply). Various failure theories are presented each requiring that stresses/strains be quantified on a ply-by-ply basis in order to make failure predictions. Both applied loads and hygrothermal (thermal and moisture) effects are treated in the computational procedure. Computer results presented herein have been produced using the LAMCALCS computer program. Use of the program is demonstrated through sample input and output descriptions. Stress and failure predictions are an important part of the process required in the design of laminated composite structures.

It is important to note a limitation on the computational methodology presented in this course. Stress predictions from classical lamination theory are quite accurate in locations away from boundaries, e.g., free edges, edge of a hole or cutout, etc., of the laminate. Thus at distances equal to the laminate plate(shell) thickness or greater, the computational method presented herein is accurate and useful in the preliminary design of laminated composite structures. The basis for this limitation is that lamination theory assumes a generalized state of plane stress which is reasonably accurate away from boundaries. Along boundaries, the state of stress becomes three-dimensional with the possibility that interlaminar shear and/or interlaminar normal stresses can become significant. Deviation of lamination theory along laminate boundaries is often referred to as a boundary-layer phenomenon. Computation of stresses along laminate boundaries is generally accomplished through the application of finite difference, finite element or boundary element method computer programs and is beyond the scope of the methodology presented in this course.

Course Content

This course is in the following PDF document:

Stress and Failure Analysis of Fiber-Reinforced Composite Structures with Computer-Based Solutions (Emphasis on Classical Lamination Theory)

Software (LAMCALC4.exe) (See Note 1)

Please click on the above underlined hypertext to view, download or print the document for your study. Because of the large file size, we recommend that you first save the file to your computer by right clicking the mouse and choosing "Save Target As ...", and then open the file in Adobe Acrobat Reader. If you still experience any difficulty in downloading or opening this file, you may need to close some applications or reboot your computer to free up some memory.

Note 1: When clicking on the software LAMCALC4.EXE, the Windows 7 operating system provides a prompt of the following type "Do you want to run or save Lamcalc4.exe from www.pdhcenter.com". The user should select "Save As" and save the software to the DESKTOP. From that point on, the user can run the software from their DESKTOP and when the program is run the OUTPUT file goes directly to the DESKTOP. Each time the program is run, the OUTPUT file should be renamed by the user and saved in an appropriate file. See section 9.0 of the course writeup with regard to saving the stress plot for later pasting into the OUTPUT file.

Course Summary

A well established computational method, based on classical lamination theory, for calculating stresses/strains in reinforced laminated composite structures has been presented. Furthermore, various failure theories have been defined, each of which utilizes the calculated stresses/strains on a ply-by-ply basis in the laminate. Externally applied loads and hygrothermal (thermal and moisture) effects have been included in the computational procedure. Computer results presented herein have been produced using the LAMCALCS computer program. Use of the program is demonstrated through sample input and output descriptions. Stress and failure predictions are an integral part of the design process when specifying laminate geometries.

It has been noted that stress predictions from classical lamination theory are quite accurate in locations away from boundaries, e.g., free edges, edge of a hole or cutout, etc., of the laminate. Thus at distances equal to the laminate plate thickness or greater the computational method presented herein is accurate and useful in the preliminary design of laminated composite structures. The basis for this limitation is that lamination theory assumes a generalized state of plane stress which is reasonably accurate away from boundaries. Along boundaries, the state of stress becomes three-dimensional with the possibility that interlaminar shear and/or interlaminar normal stresses can become significant. Deviation of lamination theory along laminate boundaries is often referred to as a boundary-layer phenomenon. Computation of stresses along laminate boundaries is generally accomplished through the application of finite difference, finite element or boundary element computer programs and is beyond the scope of the methodology presented in this course.

Quiz

Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.

DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.